Question

PLS HELP 50 POINTS

In the figure shown, which pair of angles must be complementary?

A. ∠AXD and ∠DXC

B. ∠AXY and ∠YXB

C. ∠DXC and ∠BXC

D. ∠AXB and ∠BXC

Answer 1

Answer:

$B. \text{ } \angle AXY \text{ and } \angle YXB$

Skills needed: Angle Geometry

Step-by-step explanation:

1) We are given a diagram and are asked about complementary angles.

We must fully understand this term prior to solving this problem.

---> Complementary angles are angles that add up to a measure of 90 degrees. Essentially, two complementary angles make up a right angle.

2) Let's find all right angles in the diagram.

--> $\angle BXC$ is the only marked right angle, but there are 3 others.

$\angle {BXD}$ is a straight angle, since $\overline{BD}$ is a straight line.

---> A straight angle has a measure of $180\textdegree$.

$\angle BXC + \angle CXD = \angle BXD$ as seen in the diagram.

Given $\angle BXC$ is 90 degrees (since it's a right angle), and $\angle{BXD}$ is 180 degrees (since it's a straight angle), we can solve for $\angle{CXD}$

$90+ \angle CXD =180 \\ \angle CXD=90$

This means ANGLE CXD is a right angle.

We can do this process 2 more times. Using the fact that $\overline{CA}$ is a straight line (so $\angle CXA = 180\textdegree$), we can determine that $\angle{BXA}$ and $\angle{DXA}$ are both right angles.

3) Now let's see if there are any two angles that combine to make a right angle.

$\angle{BXC}, \angle{DXC}, \text{ and } \angle{DXA}$ all are not split.

$\angle{BXA}$ however, is split into two angles ($\angle{YXB}\text{ and } \angle AXY$

These two angles would be complementary as they make up a right angle. $B$ is the answer.

Answer 2

What can you see in image?

• A co-ordinate plane
• AC a straight line

This is enough to find ans

Now

• <axb and <axc are linear pairs so their sum is 180°

One angle is 90° so other must be 90

• Complementary angles are of 90°

Hence.

• <axd and <dxc are complementary